Past Seminars- Analysis

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  • Xinan Ma
    Tue May 24, 2016
    3:00 pm
    For the Dirichlet problem on the k Hessian equation, Caffarelli-Nirenberg-Spruck (1986) obtained the existence of the admissible classical solution when the smooth domain is strictly k-1 convex in R^n. In this talk, we prove the existence of a classical admissible solution to a class of Neumann boundary value problems for k Hessian equations...
  • Yu Yuan
    Tue May 10, 2016
    3:00 pm
    We survey some new and old, positive and negative results on a priori estimates, regularity, and rigidity for special Lagrangian equations with or without certain convexity. The "gradient" graphs of solutions are minimal or maximal Lagrangian submanifolds, respectively in Euclidean or pseudo-Euclidean spaces. In the latter pseudo-...
  • Siqi Fu
    Thu Apr 21, 2016
    4:00 pm
    In this expository talk we will discuss aspects of spectral theory of the complex Laplacian, revolving around the notion of positivity.  We will discuss geometric/potential theoretic characterizations for positivity of the complex Neumann Laplacian and explain some applications of the theory in complex geometry.
  • Yuan Yuan
    Thu Mar 31, 2016
    3:00 pm
    We will discuss the common submanifolds of two Hermitian symmetric spaces. In particular, we proved that the Euclidean space and a bounded symmetric domain cannot share a common submanifold. This is based on the joint work with Professor X. Huang.
  • Robin Graham
    Tue Feb 16, 2016
    3:00 pm
    Geodesics in hyperbolic space, or more generally in an asymptotically hyperbolic manifold, have infinite length as they approach the boundary at infinity.  Nonetheless, it is possible to associate a finite renormalized length to such a geodesic.  This talk will describe how one can recover the infinite order boundary jet of an...
  • Josh Strong
    Tue Feb 9, 2016
    3:00 pm
    One way to classify bounded domains of several complex variables is to determine the boundary behavior.  It is a conjecture of Greene and Krantz that if an automorphism orbit accumulates at the boundary of a smooth domain, then that point is of finite type in the sense of D'Angelo.  We will discuss some supporting results and a...
  • Lizaveta Ihnatsyeva
    Tue Nov 24, 2015
    4:00 pm
    In the talk we consider inequalities of Hardy type for functions in Triebel-Lizorkin spaces. In particular, we discuss these inequalities for functions defined on domains whose boundary has the small Aikawa dimension  (the case of a 'thin' boundary). We also show the validity of Hardy inequalities on open sets under a combined fatness...